This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A385474 #23 Aug 01 2025 08:59:34
%S A385474 1,7,76,991,14281,219172,3512440,58096591,984340003,16996883887,
%T A385474 298017184048,5291703108292,94961611382860,1719543577996888,
%U A385474 31379622840361696,576519956457976495,10655055147825932119,197959348525977645781,3695112941037246866044
%N A385474 Expansion of (1/x) * Series_Reversion( x * (1-2*x)^2 / (1+x)^3 ).
%H A385474 <a href="/index/Res#revert">Index entries for reversions of series</a>
%F A385474 a(n) = (1/(n+1)) * Sum_{k=0..n} 2^(n-k) * binomial(3*(n+1),k) * binomial(3*n-k+1,n-k).
%F A385474 a(n) = (1/(n+1)) * [x^n] ( (1+x)^3 / (1-2*x)^2 )^(n+1).
%o A385474 (PARI) my(N=20, x='x+O('x^N)); Vec(serreverse(x*(1-2*x)^2/(1+x)^3)/x)
%o A385474 (PARI) a(n) = sum(k=0, n, 2^(n-k)*binomial(3*(n+1), k)*binomial(3*n-k+1, n-k))/(n+1);
%Y A385474 Cf. A064063, A385475.
%Y A385474 Cf. A384950.
%K A385474 nonn
%O A385474 0,2
%A A385474 _Seiichi Manyama_, Aug 01 2025